arxiv_ml 90% Match Theoretical Research Researchers in graph algorithms and machine learning,Data scientists working on clustering and segmentation 20 hours ago

Probabilistic Graph Cuts

graph-neural-networks › graph-learning

📄 Abstract

Abstract: Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and principled gradients. We present a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut. Our framework provides tight analytic upper bounds on expected discrete cuts via integral representations and Gauss hypergeometric functions with closed-form forward and backward. Together, these results deliver a rigorous, numerically stable foundation for scalable, differentiable graph partitioning covering a wide range of clustering and contrastive learning objectives.

Key Contributions

This paper unifies probabilistic relaxations for graph cuts, extending beyond RatioCut to include Normalized Cut, providing a rigorous and numerically stable framework. It offers tight analytic upper bounds and closed-form gradients, enabling scalable, end-to-end, and online learning for various clustering and contrastive learning objectives.

Business Value

Facilitates more robust and scalable clustering and segmentation tasks in areas like image analysis and data mining, enabling end-to-end trainable systems.

Paper Metadata

Innovation Type

Algorithmic Framework

Deployment Feasibility

High, as it provides a theoretical foundation and algorithmic tools for differentiable graph partitioning.

Limitations Addressed

Prior probabilistic relaxations for graph cuts were limited (e.g., to RatioCut), lacked general guarantees, and had issues with principled gradients. This work provides a unified framework with theoretical guarantees and stable gradients for a broader class of cuts.

Performance Gains

Enables scalable, differentiable graph partitioning for clustering and contrastive learning objectives.

Technical Tags

probabilistic graph cutsdifferentiable clusteringspectral clusteringnormalized cutintegral representationsGauss hypergeometric functionsend-to-end learningonline learningcontrastive learning

Research Topics

Graph TheoryClustering AlgorithmsDifferentiable OptimizationMachine Learning TheoryRepresentation Learning

Methods & Architectures

Probabilistic relaxation of graph cutsIntegral representationsGauss hypergeometric functionsDifferentiable graph partitioning

Applications & Tasks

Machine Learning Computer Vision Data Mining ClusteringGraph PartitioningRepresentation Learning Graph cut optimizationDifferentiable clusteringContrastive learning

Related Fields

Graph TheoryMachine LearningComputer VisionOptimization

Keywords

probabilistic graph cutsdifferentiable clusteringspectral clusteringnormalized cutgraph partitioningintegral representationsGauss hypergeometric functionsend-to-end learningonline learningcontrastive learningdata miningcomputer vision

Academic Context

#Graph Theory#Clustering Algorithms#Differentiable Optimization#Machine Learning Theory#Representation Learning

Commercial Potential

Target Industries

TechnologyData AnalyticsComputer Vision

Use Case Examples

Image segmentationCommunity detection in networksFeature learning for downstream tasks

Competitive Edge

Provides a more general, theoretically grounded, and differentiable alternative to traditional spectral clustering methods.

Resource Requirements

Compute Needs

Moderate, depends on graph size and complexity.

Data Requirements

Graph data.

Deployment Constraints

Scalability for very large graphs might still be a concern.

Scalability

Aims for scalable solutions through differentiable methods.

Production Readiness

Maturity Level

Theoretical Framework

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